Dear Xiang,
Wu Xiang wrote:
> Method one (getting learning effect after modeling):
> Model each block as a "condition". Then test increasement with contrast
> [3 1 1 3] or test decreasement with [3 1 1 3].
>
> Q1: Is there difference between contrasts [3 1 1 3] and [1 0.5 0.5 1]?
Yes. The increment in the first contrast is 2, whereas in the second
contrast is it not constant (the increment between 0.5 and 0.5 is 1, and
it is 0.5 elsewhere). To make the second one equivalent to the first use
[1.5:1.5].
>
> Method two (getting learning effect while modeling)
> Model all the 4 blocks as one "condition", and another parametric
> regressor with [1 2 3 4] for increasement or [4 3 2 1] for decreasement.
> Then test this parametric regressor by assign value 1 to it in contrast.
>
> Q2: Is there difference between contrasts [1 2 3 4], [2 4 6 8] or [3 1
> 1 3]?
In SPM, the parametric modulation are meancorrected (among other things,
e.g. orthogonalization w.r.t to the onset regressor, Euclidean
normalization). Thus, [2:2:8] and [3:2:3] are equivalent and will yield
the same results. The increment in both cases is 2.
[1:4] increments by 1 and will get you the same effect, but the size of the
beta will be different (it should be half as large). (The size of the beta
scales with the regressors.)
> Q3: I am not sure whether the learning effect is increasement or
> decreasement, but they may both be possible, or each one for different
> brain regions. Should I add both of the two parametric regressors, [1 2
> 3 4] and [4 3 2 1], in one model? Or I must define two models for the
> two parametric regressors separately?
No. Just put one of them as a parametric modulation in your model. When
testing for an increase you put a 1 on that regressor in your contrast,
when testing for a decrease you put a 1 in your contrast.
>
> Q4: I am using SPM5. It seems that there are two options for parametric
> regressors, "Time Modulation" and "Parametric Modulation", which one
> should I use? In addition, what values should I assign to the option,
> e.g, just a vector [1 2 3 4] here?
"Time Modulation" will just model an increase over all event in a single
regressor. If you use a polynomial expansion of 1, you will get the linear
increase. A polynomial expansion of 2 will give you the quadratic trend. In
fact, when choosing a polynomial expansion of 2, you always get 2
parametric modulators: one for the linear trend, and the second one for the
quadratic trend. Keep in mind, however, that the linear trend in
orthogonalized w.r.t. to the onset, and the quadratic trend is
orthogonalized w.r.t to the linear trend and the onset. Thus, the quadratic
trend does not look like a usual 2nd order polynomial. (Have a look at
spm_orth.m to see the implementation).
A parametric modulation does not impose a strictly monotonic trend over all
events in a regressors and is thus also suitable for measures like reaction
times. There you have yo supply a vector of parametric values, one for each
event in the onset regressor.
In you specific case (simply testing for linear/quadratic increases) you
can use both types of modulations.
>
> Q5: There are some discussion about whether the above two methods are
> equivalent. I am not a statistical expert, but for me, method one is
> flexible and would save much time, after getting the beta value of the 4
> blocks, I can do many tests using different contrasts, such as quadratic
> trend. While for method two, changing a parametric regressor means
> reestimate the model, given the slow speed of spm(matlab), I can't
> image how long it would take to find a suitable trend.
> So, my question is, are both of the two methods acceptable by the
> literature?
Well, to answer your question, both methods are acceptable.
Second point. If the effects are robust, both methods should yield almost
identical results.
Modeling each event in separate regressors will give you more flexibility
when testing different contrasts, but it will also consume more degrees of
freedom (which is usually not an issue at the first level analyses because
of abundant number of scans).
Modeling a learning effect as a parametric modulator constraints the model
to a higher degree and will thus increase the "inferential power" of your
results. You can think of it this way: with parametric modulators you are
looking for strictly linear (or quadratic) increases (or decreases) and
that is what you are most sensitive for. So if your scientific theory
clearly predicts this trend (and you find it in your data), you can be much
more certain that there actually is a linear increase. In contrast, a
linear increase that spans across different regressors can also show a
significant effect, even if one of the betas is not following the linear
trend. To really make this claim in a model with different regressors, you
would have to plot the effect sizes (beta) for each event type.
Finally, with only 4 blocks in which learning can occur, it is very hard to
*reliably* discriminate between linear and quadratic increases (or
decreases), because the trend look almost identical. So finding a suitable
trend is probably not that difficult, since you can probably only make the
case for general increases of decreases leaving the shape of the trend aside.
Cheers,
Jan
>
> Thanks
> Xiang
>

Jan Gläscher, Ph.D. Div. Humanities & Social Sciences
+1 (626) 3953898 (office) Caltech, Broad Center, M/C 11496
+1 (626) 3952000 (fax) 1200 California Blvd
[log in to unmask] Pasadena, CA 91125
